Finite Group Databasebeta

← #29695497

Subgroups — #29695497

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840406C211yesmaximal, characteristic
2C2×#16839830C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446634C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446240C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21446124C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic, complemented
18C23×#92418C2211yescharacteristic
19#16840406—24no—
20#16840406C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519746—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32C22×C22⋊Dic61—21no—
33#16839830—24no—
34C2×#14519706C2211yescharacteristic, complemented
35#16839760—24no—
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519698—24no—
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519689C2211yescharacteristic, complemented
46C2×#14519687C2211yescharacteristic, complemented
47#16839659—21no—
48#16839636—21no—
49#16839634—21no—
50#16839631C2211yescharacteristic, complemented
51#16839619C2211yescharacteristic, complemented
52C4⋊C4×Dic61C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C23×Dic61—21no—
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—41no—
82C22×#92418—22no—
83C22×#92418—22no—
84C22×#92418—41no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87#14519764—22no—
88#14519764C2×C414yescomplemented
89#14519758—28no—
90#14519756—22no—
91#14519756C2×C414yescomplemented
92#14519749—28no—
93#14519748—22no—
94#14519748C2×C414yescomplemented
95#14519746—28no—
96D4×Dic61—22no—
97D4×Dic61C2×C414yescomplemented
98C4×C22⋊D61C2×C414yes—
99C4×C22⋊D61D414yes—
100#14519737—44no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C4⋊C4×D61—22no—
113C4⋊C4×D61—41no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—28no—
120C2×C22⋊Dic61D411yescharacteristic
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519702—22no—
127#14519702—41no—
128#14519700—22no—
129#14519700—41no—
130#14519698—22no—
131#14519698—22no—
132#14519698—22no—
133#14519698D414yescomplemented
134#14519689—22no—
135#14519687—22no—
136#14519684—21no—
137#14519684—21no—
138C25×C61—21no—
139C22×D4×C61—22no—
140C22×D4×C61—22no—
141C22×D4×C61—21no—
142C22×D4×C61—22no—
143C22×D4×C61—41no—
144C22×D4×C61—41no—
145C22×D4×C61C2×C414yescomplemented
146C22×D4×C61C2311yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—41no—
157#102×C61—41no—
158C22⋊C8×C61—22no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—24no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—81no—
168C24×C61—81no—
169C24×C61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×D4×C61—28no—
172C2×D4×C61—24no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—44no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C22×C412yes—
188C2×D4×C61C2×D412yes—
189C2×D4×C61#4112yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61C22⋊C414yes—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—24no—
214C22×Dic61—21no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61—42no—
219C22×Dic61—81no—
220C22×Dic61—81no—
221C22×Dic61—81no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758224—28no—
226#11758224—44no—
227#11758224—44no—
228#11758224—44no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C2×D412yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C22⋊C4×C61—42no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61C22⋊C414yes—
261#11758198—42no—
262#11758198C22⋊C414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—42no—
268C4⋊Dic61C22×C412yes—
269C4⋊Dic61C2×D412yes—
270#11758196—24no—
271#11758196—42no—
272#11758196—42no—
273#11758196—81no—
274#11758196C22⋊C414yes—
275C4×Dic61—42no—
276C4×Dic61C22×C412yes—
277C4×Dic61C2×D412yes—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—44no—
284C2×#92418C2×D412yes—
285#11758189—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—48no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—48no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61—84no—
309C23×C61—84no—
310C23×C61—84no—
311C23×C61C2×C22⋊C412yes—
312C23×C61AGL(1,ℤ/8)12yes—
313C23×C61#13712yes—
314C23×C61C22×D411yescharacteristic
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61C2×C22⋊C412yes—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—48no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61C4×D414yescomplemented
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61C2×C22⋊C412yes—
344C2×C4×C61C23×C411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C22⋊D61—28no—
351C22⋊D61—48no—
352C22⋊D61—84no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—48no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—84no—
373C2×Dic61—84no—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61C2×C22⋊C412yes—
376C2×Dic61C2×C22⋊C412yes—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386C8×C61—41no—
387C8×C61—41no—
388#92418—22no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—24no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—816no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61#41714yescomplemented
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61D4211yescharacteristic
415C22×C61#54611yescharacteristic
416C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C61C2×#13711yescharacteristic
418C22×C61#57611yescharacteristic
419C22×C61#57711yescharacteristic
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C4×C61—22no—
428C4×C61—81no—
429C4×C61—81no—
430C4×C61C2×C4×D411yescharacteristic
431C4×C61#51811yescharacteristic
432C4×C61D4211yescharacteristic
433C4×C61#54611yescharacteristic
434Dic61—22no—
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61—42no—
439Dic61—42no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786D6111yescharacteristic, complemented
455#1762—611no—
456C2×C61—24no—
457C2×C61—44no—
458C2×C61—82no—
459C2×C61D4×C22⋊C411yescharacteristic
460C2×C61C2×#41711yescharacteristic
461C2×C61#289711yescharacteristic
462C2×C61#326411yescharacteristic
463C2×C61#326611yescharacteristic
464C2×C61#330611yescharacteristic
465C2×C61#331411yescharacteristic
466D61—42no—
467C22×#41—611no—
468C23×D4C2×D6111yescharacteristic
469C22×M16—611no—
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—611no—
481C2×C4×D4—1221no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—1224no—
497C2×#102C2×D6111yescharacteristic
498C2×#102C2×D6111yescharacteristic
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8C2×D6111yescharacteristic
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380C2×D6111yescharacteristic
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—22no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—611no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4C4×D6114yescomplemented
534C22×D4C22×D6111yescharacteristic
535C22×D4C22×D6111yescharacteristic
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1222no—
548C22×C8—1222no—
549C22×C8—2441no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1228no—
559#121—1222no—
560#120—1228no—
561C4×D4—614no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4—2444no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—1228no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—22no—
599#102—22no—
600#102—41no—
601#102—41no—
602#102—614no—
603#102—1222no—
604#102—1222no—
605#102—1222no—
606C22⋊C8—22no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—21no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24—611no—
622C24D4×D6111yescharacteristic
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—28no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—24no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—614no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—4881no—
654C2×D4—4881no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4C2×C4×D6112yes—
658C2×D4C2×C4×D6112yes—
659C2×D4D4×D6112yes—
660C2×D4#1175822412yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—1224no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—4881no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—4881no—
686C22×C4—2442no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4C2×C4×D6112yes—
693C22×C4D4×D6112yes—
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—612no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2444no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—614no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1224no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—4881no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4—2442no—
726C22⋊C4—42no—
727C22⋊C4—614no—
728C22⋊C4—614no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—612no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23C22⋊C4×D6112yes—
771C23#1451980112yes—
772C23#1451980612yes—
773C23C2×D4×D6111yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—41no—
785D4—41no—
786D4—1228no—
787D4—4884no—
788D4—2448no—
789D4#1451973714yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—612no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—4884no—
819C2×C4—4884no—
820C2×C4—4884no—
821C2×C4—2448no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4C2×#1175822411yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982211yescharacteristic
838C8—41no—
839C8—41no—
840C8—1222no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—1222no—
864C22—1222no—
865C22—1222no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22—2441no—
870C22#1683976014yescomplemented
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684039411yescharacteristic
873C22#1684039911yescharacteristic
874C22C2×#1451980111yescharacteristic
875C22C2×#1451980611yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057211yescharacteristic
878C4—22no—
879C4—81no—
880C4—81no—
881C4—1222no—
882C4—1222no—
883C4—1222no—
884C4—4881no—
885C4—2442no—
886C4—2442no—
887C4—2442no—
888C4C2×#1451973711yescharacteristic
889C4#1684023511yescharacteristic
890C4#1684039411yescharacteristic
891C4#1684039911yescharacteristic
892C2—24no—
893C2—44no—
894C2—82no—
895C2—2442no—
896C2#2144863511yescharacteristic
897C2C2×#1683976011yescharacteristic
898C2#2145434411yescharacteristic
899C2#2145729211yescharacteristic
900C2#2145733311yescharacteristic
901C2#2145778411yescharacteristic
902C2#2145790411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839830C2semidirect
3. C2×#16839760C2semidirect
4. C22×#14519698C2semidirect
5. #21448715C2semidirect
6. #21446750C2semidirect
7. #21446634C2semidirect
8. #21446254C2semidirect
9. #21446240C2semidirect
10. #21446133C2semidirect
11. #21446124C2semidirect
12. #21445817C2semidirect
13. #21445756C2semidirect
14. #21445646C2semidirect
15. C61×#1786C2semidirect
17. C22×#11758189C22semidirect
20. #16840406C4semidirect
31. C2×C4⋊C4×D61C22semidirect
34. C2×#14519706C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
45. C2×#14519689C22semidirect
46. C2×#14519687C22semidirect
50. #16839631C22semidirect
51. #16839619C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
69. C2×#11758224C2×C4semidirect
88. #14519764C2×C4semidirect
91. #14519756C2×C4semidirect
94. #14519748C2×C4semidirect
97. D4×Dic61C2×C4semidirect
133. #14519698D4semidirect
145. C22×D4×C61C2×C4semidirect
330. D4×C61C4×D4semidirect
412. C22×C61#417semidirect
454. #1786D61semidirect
515. C61#22419semidirect
533. C22×D4C4×D61semidirect
789. D4#14519737semidirect
870. C22#16839760semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404062
C2×#168398302
C2×#168397602
C22×#145196982
#214487152
#214467502
#214466342
#214462542
#214462402
#214461332
#214461242
#214458172
#214457562
#214456462
C61×#17862
#2241961